BUAL 2650 FINAL EXAM – LEE
QUESTIONS & ANSWERS(RATED
A+)
Simple Regression - ANSWER-only 1 predictor variable
-y-hat=b0 + b1*x
Multiple Regression - ANSWER-more than 1 predictor variables
-y-hat=b0 + b1*x1 + b2*x2......
Residual - ANSWERthe difference between the actual data and the value we predict
for it
=observed-predicted
=y-y-hat
Interpreting Residuals - ANSWER-Negative residual: the regression equation
provided an overestimate of the data.
-Positive residual: the regression equation provided an underestimation of the data.
Linear regression only works for... - ANSWERLinear models
What do we want to see from a residual plot? - ANSWER-No pattern
-No plot thickening
-Randomization
Extrapolation - ANSWER-venturing into new x territory
-used to estimate values that go beyond a set of given data or observations
-very dangerous
Dangers of Extrapolation - ANSWER-assumes there is a linear relationship beyond
the range of the data
-assumes that nothing about the relationship between x and y changes at extreme
values of x
Adjusted R-squared - ANSWERAdjusted R-squared imposes a 'penalty' for each
new term that's added to the model in an attempt to make models of different sizes
comparable
Adjusted R-squared vs. R-squared - ANSWERAdding new predictor variables will
always keep the R-squared value the same or increase it. But, even if the R-squared
value grows, that does not mean that the resulting model is a better model of that is
has greater predictive ability.
, F-Test Interpretation - ANSWER-"Since P-value < 0.0001, reject the null hypothesis.
At least one of the predictors accounts for the variation in predicting the dependent
variable"
-if the f-test is large, this is good. it means we can reject the null and conclude the
MRM is good for predicted the dependent variable
-bigger f-values mean smaller p-values
Interpreting the Intercept of a MRM - ANSWERis it meaningful or not? we decide if it
is meaningful by assuming the other coefficients are 0
Is this multiple regression model any good at all? - ANSWERTest hypotheses: HO:
all beta values = 0 vs. HA: at least 1 beta value does not = 0
-then, use a t-test
Rules for interpreting multiple regression coefficients - ANSWER-express in terms of
the units of the dependent variable
-always say "all else being equal"
-always mention the other variables by saying "after (variable #1) and (variable #2)
are accounted for," and interpret the coefficient
How do we determine if a multiple regression model is significant? - ANSWERp-
value (needs to b small) and t-test (needs to be big - this means that at least one of
the predictors accounts for the variation in predicting the dependent variable.)
R-squared - ANSWER-"Goodness of fit"
-a statistical measure of how close the data are to the fitted regression line (how well
observed outcomes are replicated by the model)
Dangers of R-squared - ANSWER
Interpreting R-Square - ANSWERR-square = .80 indicates that the model explains
80% of variability of the response (y) data OR R-square = 0.41 indicates that 41% of
the variability of height can be explained by the mode.
Outliers - ANSWERpoints with y-values far from the regression model; points far
from the body of the data
Leverage - ANSWERA data point can also be unusual if its x-value is far from the
mean of the x-values. Such points are said to have high leverage.
Influential Point - ANSWERWe say that a point is influential if omitting it from the
analysis gives a very different slope for the model
Causality Warning - ANSWERno matter how strong the association, no matter how
large the r-squared value, there is no way to conclude that for a regression alone
that one variable caused the other
Autocorrelation - ANSWERWhen values at time, t, are correlated with values at time,
t-1, we say the values are autocorrelated in the first order. If values are correlated
QUESTIONS & ANSWERS(RATED
A+)
Simple Regression - ANSWER-only 1 predictor variable
-y-hat=b0 + b1*x
Multiple Regression - ANSWER-more than 1 predictor variables
-y-hat=b0 + b1*x1 + b2*x2......
Residual - ANSWERthe difference between the actual data and the value we predict
for it
=observed-predicted
=y-y-hat
Interpreting Residuals - ANSWER-Negative residual: the regression equation
provided an overestimate of the data.
-Positive residual: the regression equation provided an underestimation of the data.
Linear regression only works for... - ANSWERLinear models
What do we want to see from a residual plot? - ANSWER-No pattern
-No plot thickening
-Randomization
Extrapolation - ANSWER-venturing into new x territory
-used to estimate values that go beyond a set of given data or observations
-very dangerous
Dangers of Extrapolation - ANSWER-assumes there is a linear relationship beyond
the range of the data
-assumes that nothing about the relationship between x and y changes at extreme
values of x
Adjusted R-squared - ANSWERAdjusted R-squared imposes a 'penalty' for each
new term that's added to the model in an attempt to make models of different sizes
comparable
Adjusted R-squared vs. R-squared - ANSWERAdding new predictor variables will
always keep the R-squared value the same or increase it. But, even if the R-squared
value grows, that does not mean that the resulting model is a better model of that is
has greater predictive ability.
, F-Test Interpretation - ANSWER-"Since P-value < 0.0001, reject the null hypothesis.
At least one of the predictors accounts for the variation in predicting the dependent
variable"
-if the f-test is large, this is good. it means we can reject the null and conclude the
MRM is good for predicted the dependent variable
-bigger f-values mean smaller p-values
Interpreting the Intercept of a MRM - ANSWERis it meaningful or not? we decide if it
is meaningful by assuming the other coefficients are 0
Is this multiple regression model any good at all? - ANSWERTest hypotheses: HO:
all beta values = 0 vs. HA: at least 1 beta value does not = 0
-then, use a t-test
Rules for interpreting multiple regression coefficients - ANSWER-express in terms of
the units of the dependent variable
-always say "all else being equal"
-always mention the other variables by saying "after (variable #1) and (variable #2)
are accounted for," and interpret the coefficient
How do we determine if a multiple regression model is significant? - ANSWERp-
value (needs to b small) and t-test (needs to be big - this means that at least one of
the predictors accounts for the variation in predicting the dependent variable.)
R-squared - ANSWER-"Goodness of fit"
-a statistical measure of how close the data are to the fitted regression line (how well
observed outcomes are replicated by the model)
Dangers of R-squared - ANSWER
Interpreting R-Square - ANSWERR-square = .80 indicates that the model explains
80% of variability of the response (y) data OR R-square = 0.41 indicates that 41% of
the variability of height can be explained by the mode.
Outliers - ANSWERpoints with y-values far from the regression model; points far
from the body of the data
Leverage - ANSWERA data point can also be unusual if its x-value is far from the
mean of the x-values. Such points are said to have high leverage.
Influential Point - ANSWERWe say that a point is influential if omitting it from the
analysis gives a very different slope for the model
Causality Warning - ANSWERno matter how strong the association, no matter how
large the r-squared value, there is no way to conclude that for a regression alone
that one variable caused the other
Autocorrelation - ANSWERWhen values at time, t, are correlated with values at time,
t-1, we say the values are autocorrelated in the first order. If values are correlated
